Unfortunately, her application apparently did not survive to be found in the records. I've run a blank.

None-the-less, there would be not much of detail to be found other than where and from what aliment caused his death. That is because he died only 25 days following his enlistment. His record consists of just one card.

C M. Rape, Private, Company F, 36th Mississippi Infantry, enlisted May 5, 1862 at Corinth by Lt. Owen for 3 years or the war, died disease May 30, 1862

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi

Note, this is not unusual, men began dying of various forms of Camp Disease soon after joining up.
What is surprising is that farm boys where more susceptible of disease than city boys who were perhaps more immune to communicable diseases.

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This regiment was composed of volunteer companies organized under a call of the Governor to assemble at Meridian, where the companies were mustered into the Confederate service. Field officers were elected March 12, 1862, Brown, Harper and Witherspoon. The regiment was in camp at Meridian during the battle of Shiloh. There was a rapid change in officers. At Rienzi, May 30, the day after the evacuation of Corinth by Beauregard's army, Witherspoon was Colonel and made a complete "list of the names of soldiers of the Thirty-sixth Regiment Mississippi Volunteers, between the ages of 18 and 35 years, including those over and under age, who have volunteered for three years or the war," which is on file in this department.*

The regiment was (with the Thirty-seventh) part of the brigade of Gen. Patton Anderson, of Ruggles' Division, Bragg's Corps, at Corinth, early in May, and took part in the engagement at Farmington, May 9. General Anderson said in his report: "A large portion of the Thirty-sixth Mississippi Regiment, although never having formed a line of battle or heard a hostile gun before, behaved with that gallantry and spirit which characterized the troops of that chivalrous State on every field." The regiment had 14 killed and wounded. It was attached to Chalmers' Brigade in return of April 28, and of May.

* Not found here

http://www.researchonline.net/mscw/unit132.htm

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1860 United States Federal Census
Name: C M Rape
Age: 28
Birth Year: abt 1832
Gender: Male
Birth Place: North Carolina
Home in 1860: District 5, Scott, Mississippi
Post Office: Hillsboro
Family Number: 17
Value of real estate: $300
Household Members:
Name Age
C M Rape 28 Farmer
C D Rape 24 born in Mississippi
N J Rape 1 -do-